This paper presents theoretical results on the relationship between density of states (DOS) and scanning tunneling microscope current-voltage curves in polymers. We considered samples of linear hydrocarbons electrically grounded at one of their extremes. The other extreme is electrically connected to the microscope tip via electron tunneling through vacuum. When a voltage, V, is applied to the tip, electric current, I, flows in the tip-sample circuit. This current varies as the voltage varies and depends on the DOS to the extent that no current would flow if no electron states exist at a certain energy (or voltage). The detailed relationship between DOS and the current-voltage (I-V) curve is not known a priori. We solve the corresponding quantum problem in the context of tight binding and find that I-V reproduces accurately the resonant energy peaks of the DOS. We apply the results to 100 atom-long alkane and alkene chains and found that there is a significant voltage shift in the corresponding curves as to discriminate one structure from the other.